During last two decades the progress in the molecular biology has led to development of “the targeted molecular therapy”, which consists of macromolecular drugs that specifically interact with a certain target cell population. This interaction is frequently mediated by a specific binding of a ligand (here and further on—any soluble substance used as a part of treatment for certain disease, e.g. drug, prodrug, etc.) to a receptor that is expressed on the cell surface (here and further on we use the term “receptor” in a broad sense—any macromolecule expressed on the cell surface, which specifically binds the mentioned ligand).
Pharmacokinetics (PK) and pharmacodynamics (PD) of ligands (both unconjugated ones and their conjugates with chemotherapeutic, enzymatic, radioactive and other agents) are complex and include PK in the blood, the perfusion—and diffusion—limited transport phenomena in the blood-tissue border, binding of ligands to their receptors, and finally their effect on the target cells (cell-mediated ligand-dependent cytotoxicity, a complement activation, an effect induced by the conjugate, a cell signaling cascade induction by an activation of the receptor upon ligand binding, etc). This complexity demands development of computational tools for optimization of drug design, treatment protocol choice and individualization of the treatment.
Several aspects of this complex process (including the perfusion, the diffusion, the tissue distribution, the conjugate efficacy) have been analyzed in the case of monoclonal antibodies by mathematical models (Jackson et al., Friedrich et al., Baxter et al.). This analysis can be very important for an evaluation of applicability of a specific monoclonal antibody (with or without a conjugate) to a certain disease prior to performing time—and resource—consuming clinical trials. However, in all cited models, description of the process of binding of a ligand (a monoclonal antibody) to their target is based solely on two values—the average number of receptors (antigens) per cell and the dissociation constant (the ratio of dissociation and the association rates between a specific monoclonal antibody and its antigen). These models do not take into account the fact that binding and dissociation of a ligand are stochastic processes, and consequently, the number of the bound antibodies can vary considerably between individual cells even if they are identical with respect to the antigen kinetics. Therefore drug efficacy can be easily over- or underestimated, rendering exact quantitative predictions of the in vivo effect highly unreliable.